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--- courses:phy101l:2 [2023/06/17 10:04] – asad
+++ courses:phy101l:2 [2023/10/15 04:02] (current) – asad
@@ Line 1: / Line 1: @@
 ====== 2. Gravitational acceleration from a pendulum ======
+[[https://colab.research.google.com/drive/1XMSfX646Gj-83531zYt1wXZ8RA0N1uOP?usp=sharing|Click here for the report sample]]
 ===== - Introduction and theory =====
+{{https://upload.wikimedia.org/wikipedia/commons/thumb/f/f7/Forces_acting_on_a_simple_pendulum.svg/807px-Forces_acting_on_a_simple_pendulum.svg.png?nolink&500}}
+For a simple pendulum
+$$ T = 2\pi \sqrt{\frac{L}{g}} \Rightarrow g = 4\pi^2 \frac{L}{T^2}. $$
+For a compound pendulum
+$$ T = 2\pi \sqrt{\frac{\frac{K^2}{l}+l}{g}} $$
+and, hence, a compound pendulum is equivalent to a simple pendulum if
+$$ L = \frac{K^2}{l} + l \Rightarrow l^2 - lL + K^2 = 0 $$
+which is a quadratic equation with two solutions $l_1$ and $l_2$ where $l_1+l_2=L$ and $l_1l_2=K^2$.
+You have to find gravitational acceleration $g$ and radius of gyration $K=\sqrt{l_1l_2}$.
 ===== - Method and data =====
-===== - Analysis and results =====
+==== - Data table ====
+^ Hole no. ^ Distance [cm] ^ Trial ^ Time for 10 oscillations [s] ^
+| 1 | 10 | 1 |  |
+|:::|:::| 2 |  |
+| 2 | 20 | 1 |  |
+|:::|:::| 2 |  |
+| 3 | 30 | 1 |  |
+|:::|:::| 2 |  |
+| 4 | 40 | 1 |  |
+|:::|:::| 2 |  |
+| 6 | 60 | 1 |  |
+|:::|:::| 2 |  |
+| 7 | 70 | 1 |  |
+|:::|:::| 2 |  |
+| 8 | 80 | 1 |  |
+|:::|:::| 2 |  |
+| 9 | 90 | 1 |  |
+|:::|:::| 2 |  |
+===== - Graphical analysis =====
+===== - Calculating g =====
+Find $R$ from here: https://rechneronline.de/earth-radius
+$$ g = \frac{GM}{R^2} $$
 ===== - Discussion and conclusion =====
+Answer the following questions in Discussion.
+  - Why the angle of deflection of the pendulum should not be large?
+  - Why are the periods at 10, 30, 70 and 90 cm similar?
+  - Why do you get two symmetric curves after plotting $T$ as a function of $l$.
+  - If your were periods at 10, 30, 70 and 90 cm were not as similar as expected, discuss why this happened?